On a Classical, Geometric Origin of Magnetic Moments, Spin-Angular Momentum and the Dirac Gyromagnetic Ratio

By treating the real Maxwell Field and real linearized Einstein equations as being imbedded in complex Minkowski space, one can interpret magnetic moments and spin-angular momentum as arising from a charge and mass monopole source moving along a complex world line in the complex Minkowski space. In the circumstances where the complex center of mass world-line coincides with the complex center of charge world-line, the gyromagnetic ratio is that of the Dirac electron.Comment: 17 page

Optimization in Gradient Networks

Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural correlations and strongly reduce congestion occurring on the network by using a Monte Carlo optimization scheme. This optimization alters the degree distribution and other structural properties of the resulting gradient networks. These results are expected to be relevant for transport and other dynamical processes in real network systems.Comment: 5 pages, 4 figure

A user's manual for the method of moments Aircraft Modeling Code (AMC)

This report serves as a user's manual for the Aircraft Modeling Code or AMC. AMC is a user-oriented computer code, based on the method of moments (MM), for the analysis of the radiation and/or scattering from geometries consisting of a main body or fuselage shape with attached wings and fins. The shape of the main body is described by defining its cross section at several stations along its length. Wings, fins, rotor blades, and radiating monopoles can then be attached to the main body. Although AMC was specifically designed for aircraft or helicopter shapes, it can also be applied to missiles, ships, submarines, jet inlets, automobiles, spacecraft, etc. The problem geometry and run control parameters are specified via a two character command language input format. The input command language is described and several examples which illustrate typical code inputs and outputs are also included

A user's manual for the Electromagnetic Surface Patch code: ESP version 3

This report serves as a user's manual for Version III of the Electromagnetic Surface Patch Code or ESP code. ESP is user-oriented, based on the method of moments (MM) for treating geometries consisting of an interconnection of thin wires and perfectly conducting polygonal plates. Wire/plate junctions must be about 0.1 lambda or more from any plate edge. Several plates may intersect along a common edge. Excitation may be by either a delta-gap voltage generator or by a plane wave. The thin wires may have finite conductivity and also may contain lumped loads. The code computes most of the usual quantities of interest such as current distribution, input impedance, radiation efficiency, mutual coupling, far zone gain patterns (both polarizations) and radar-cross-section (both/cross polarizations)

A user's manual for the Loaded Microstrip Antenna Code (LMAC)

The use of the Loaded Microstrip Antenna Code is described. The geometry of this antenna is shown and its dimensions are described in terms of the program outputs. The READ statements for the inputs are detailed and typical values are given where applicable. The inputs of four example problems are displayed with the corresponding output of the code given in the appendices

Second look at the spread of epidemics on networks

In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semi-directed random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly-connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In an appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure

Mean-field solution of the small-world network model

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.Comment: 14 pages, 2 postscript figure

The first-mover advantage in scientific publication

Mathematical models of the scientific citation process predict a strong "first-mover" effect under which the first papers in a field will, essentially regardless of content, receive citations at a rate enormously higher than papers published later. Moreover papers are expected to retain this advantage in perpetuity -- they should receive more citations indefinitely, no matter how many other papers are published after them. We test this conjecture against data from a selection of fields and in several cases find a first-mover effect of a magnitude similar to that predicted by the theory. Were we wearing our cynical hat today, we might say that the scientist who wants to become famous is better off -- by a wide margin -- writing a modest paper in next year's hottest field than an outstanding paper in this year's. On the other hand, there are some papers, albeit only a small fraction, that buck the trend and attract significantly more citations than theory predicts despite having relatively late publication dates. We suggest that papers of this kind, though they often receive comparatively few citations overall, are probably worthy of our attention.Comment: 7 pages, 3 figure

Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.Comment: 13 pages, 2 figure